The majority of drugs used in cancer therapy cause suppression of blood cell formation in the bone marrow. The most important effects of that suppression are the risk of serious infection due to low white blood cells and bleeding due to low platelets. Substances called cytokines or hematopoietic growth factors are proteins which can stimulate the bone marrow to produce more of these cells. SC-70935 is a cytokine and may be able to reduce the duration of the low white blood cell or platelet counts after chemotherapy. It could therefore also reduce the risk of bacterial and fungal infection and thus the need for hospitalization for antibiotic therapy, and/or the risk of bleeding and the need for platelet transfusions. Subjects will be recruited from patients between 2 and 21 years of age with recurrent or progressive solid tumors, refractory to conventional treatment, or newly-diagnosed patients for whom the chemotherapy agents used in this study are considered standard. Patients will be treated with standard chemotherapy and will receive the study drug by subcutaneous injection starting one day after the chemotherapy course and continuing for up to 14 days or until the white blood count and/or platelet counts are adequate.